Question

A health psychologist working a in nursing home believes that personal control is associated with feelings of well-being. In a field experiment, residents on one floor of the nursing home were given opportunities for personal control in their lives; e.g., arrange their own furniture, decide how to spend free time, choose and take care of a plant, etc. In another floor, residents were treated as usual. After a month the residents are asked to fill out a feelings of well-being survey where higher scores indicate more well-being. What can the psychologist conclude with α = 0.05? The data are below.

personal control	no personal control
12 12 12 6 17 14 13 11 13 13	13 12 11 10 11 10 11 11 13 11

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Condition 1:
---Select--- well-being no personal control personal control nursing home field experiment
Condition 2:
---Select--- well-being no personal control personal control nursing home field experiment

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

Residents with personal control showed significantly more feelings of well-being than those with no personal control.Residents with no personal control showed significantly more feelings of well-being than those with personal control.    There is no significant well-being difference between residents with personal control and no personal control.

Answer 1

A)Since the samples are independent , one is from first floor and other from second , the appropriate test is independent samples t test

B)Condition 1 : well being is not affected by personal control in the nursing home field experiment

Condition 2:well being is affected by personal control in the nursing home field experiment

C)H₀: There is no significant difference in well being due to personal control

H_a : There is signusignif difference in well being due to personal control

Test statistic :

The value of test statistic is 1.073

p value is 0.298

Since p value is more than 0.05,we fail to reject H₀

D) Corresponding effect size

Cohen's d = (M₂ - M₁) ⁄ SD_pooled

where:

SD_pooled = √((SD₁² + SD₂²) ⁄ 2)

d= 0.4798

Magnitude : small effect

r2 = t²/(t²+df) =.0601

Magnitude = small effect

E)There is no significant well-being difference between residents with personal control and no personal control.